The present invention relates generally to peristaltic pumps which are used to pump fluids through resilient tubes. More particularly, the present invention relates to the drive mechanism of a linear peristaltic pump and to the arrangement for a mechanical compensator which minimizes the force that can be exerted by the peristaltic mechanism against the tube. The present invention is particularly, but not exclusively, useful in the health care field for the intravenous administration of medical solutions to patients.